OSTBC Combiner

Combine inputs using orthogonal space-time block code

• 

Libraries:
Communications Toolbox / MIMO

Description

The OSTBC Combiner block combines the input signal (from all of the receive antennas) and the channel estimate signal to extract the soft information of the symbols encoded by an orthogonal space-time block code (OSTBC). The input channel estimate does not need to be constant and can vary each time you run the block. The combining algorithm uses only the estimate for the first symbol period per codeword block. A multiple-input multiple-output (MIMO) communications system applies symbol demodulation or decoding after the OSTBC combining process.

The block conducts the combining operation for each symbol independently. The combining algorithm depends on the structure of the OSTBC. For more information, see OSTBC Combining Algorithm.

Examples

OSTBC Over 3-by-2 Rayleigh Fading Channel

Simulate orthogonal space-time block codes (OSTBC) to achieve diversity gains in a multiple-input multiple-output (MIMO) communications system. The example shows the transmission of data over three transmit antennas and two receive antennas using independent Rayleigh fading per link.

Explore Model

The doc_ostc32 model creates a random binary signal, modulates it using a binary phase shift keying (BPSK) technique, and then encodes the waveform using a rate 3/4 orthogonal space-time block code for transmission over the fading channel. The fading channel has six independent links that result from the configuration of single-path Rayleigh fading processes. The simulation adds white Gaussian noise at the receiver, and then combines the signals from both receive antennas into a single stream for demodulation. For this combining process, the model assumes perfect knowledge of the channel gains at the receiver. The simulation compares the demodulated data with the original transmitted data and computes the bit error rate. The simulation runs until it processes 100 errors or 1e6 bits, whichever comes first.

Orthogonal Space-Time Block Code

This matrix shows the rate 3/4 code with three transmit antenna orthogonal space-time block code configured in the OSTBC Encoder block:

where , , and correspond to the three symbol inputs for which the output is given by the matrix. The input to the OSTBC Encoder block is a 3-by-1 vector signal and the output is a 4-by-3 matrix. The number of columns in the output signal indicates the number of transmit antennas for this simulation, where the first dimension is for time. The OSTBC Combiner block outputs a 3-by-1 vector.

For the rate 3/4 OSTBC code modeled, the output signal power per time step is 3x(3/4) = 2.25W. A channel symbol carries 3 data bits, is 4 time steps long, and has a period of 3e-3 seconds. At the receiver, two antennas result in 3/2 bits per symbol per channel (antenna). In addition,

where k is the number of bits per symbol. Since the AWGN Channel block requires per-channel values for input signal power and number of bits per symbol, set the Es/No value to EbNo+10*log10(3/2) to calibrate the white Gaussian noise added in the simulation.

Performance

Compare the performance of the model to theoretical results by using the Bit Error Rate Analysis app. This plot compares the simulated BER for a range of Eb/No values with the theoretical results for a diversity order of six.

The theoretical and simulated results align well. The variation between theoretical and simulated results is primarily due to the simulated fading channel model having a small Doppler fade. Since the simulated channel varies slightly over the block symbols, the simulated and theoretical results show some variation.

Ports

Input

Rx — Received signal

column vector | matrix | 3-D array

Received signal, specified as a matrix or 3-D array. For more information, see Input-to-Output Dimensions.

Data Types: single | double | fixed point
Complex Number Support: Yes

cEst — Channel estimate

matrix | 3-D array | 4-D array

Channel estimate, specified as a matrix or 3-D array. For more information, see Input-to-Output Dimensions.

Data Types: single | double | fixed point
Complex Number Support: Yes

Output

Out — Output data

matrix | 3-D array

Output data, returned as a matrix or 3-D array. For more information, see Input-to-Output Dimensions.

The output signal inherits the data type from the input signal. For fixed-point signals, the complex conjugation might cause overflows, which you must manage with the Saturate on integer overflow fixed-point parameter.

This port is unnamed on the block icon.

Data Types: single | double | fixed point

Parameters

To edit block parameters interactively, use the Property Inspector. From the Simulink^® Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.

Main

Number of transmit antennas — Number of transmit antennas

2 (default) | 3 | 4

Number of transmit antennas, specified as 2, 3, or 4.

Rate — Symbol rate

3/4 (default) | 1/2

Symbol rate of the code, specified as 3/4 or 1/2. When you set Number of transmit antennas to 2, the symbol rate is 1.

Dependencies

To enable this parameter, set Number of transmit antennas to 3 or 4.

Number of receive antennas — Number of receive antennas

1 (default) | integer in range [1,8]

Number of receive antennas, specified as an integer in the range [1,8].

Data Types

Rounding mode — Rounding mode for fixed-point calculations

Floor (default) | Ceiling | Convergent | Nearest | Round | Simplest | Zero

Rounding mode for fixed-point calculations, specified as Floor, Ceiling, Convergent, Nearest, Round, Simplest, or Zero. The block uses rounding method specified by this parameter to round off the calculation to a representable number if a value cannot be represented exactly by the specified data type and scaling. For more information, see Rounding (Fixed-Point Designer).

Saturate on integer overflow — Option to saturate on integer overflow

off (default) | on

For fixed-point calculations, use this parameter to specify the method to be used if the magnitude of a fixed-point calculation result does not fit into the range of the data type and scaling that stores the result.

• To saturate on integer overflow, select this parameter.

• To wrap on integer overflow, do not select this parameter.

For more information, see Precision and Range.

Data Types: Boolean

Product Output — Complex product in numerator for diversity combining

Inherit: Inherit via internal rule (default) | Inherit: Same as product output | fixdt(1,16,0) | <data type expression>

Complex product in the numerator for diversity combining, specified as Inherit: Inherit via internal rule, Inherit: Same as product output, fixdt(1,16,0), or a custom <data type expression>. For more information, see Fixed-Point Signals.

Accumulator — Summation in numerator for diversity combining

Inherit: Inherit via internal rule (default) | Inherit: Same as product output | fixdt(1,16,0) | <data type expression>

Summation in the numerator for diversity combining. Fixed-point blocks that must hold summation results for further calculation usually allow you to specify the data type and scaling of the accumulator. Most such blocks cast to the accumulator data type before summation:

Use the Accumulator >> Mode parameter to specify how you would like to designate the accumulator word and fraction lengths:

• When you select Inherit via internal rule, the accumulator output word and fraction lengths are automatically calculated for you. For more information, see Inherit via Internal Rule.

• When you select Same as product output, these characteristics match those of the product output.

• When you select Same as input, these characteristics match those of the first input to the block.

• When you select Binary point scaling, you are able to enter the word length and the fraction length of the accumulator, in bits.

• When you select Slope and bias scaling, you are able to enter the word length, in bits, and the slope of the accumulator. The bias of all signals in DSP System Toolbox™ software is zero.

Energy product output — Complex product in denominator

Inherit: Inherit via internal rule (default) | Inherit: Same as product output | fixdt(1,16,0) | <data type expression>

Complex product in the denominator for calculating total energy in the MIMO channel, specified as Inherit: Inherit via internal rule, Inherit: Same as product output, fixdt(1,16,0), or a custom <data type expression>.

Energy accumulator — Summation in denominator for calculating total energy in MIMO channel

Inherit: Inherit via internal rule (default) | Inherit: Same as accumulator | Inherit: Same as energy product output | fixdt(1,16,0) | <data type expression>

Summation in the denominator for calculating total energy in the MIMO channel, specified as Inherit: Inherit via internal rule, Inherit: Same as accumulator, Inherit: Same as energy product output, fixdt(1,16,0), or a custom <data type expression>

Division output — Normalized diversity combining by total energy in MIMO channel

Inherit: Same as accumulator | fixdt(1,16,0) | <data type expression>

Normalized diversity combining by total energy in the MIMO channel, specified as Inherit: Same as accumulator, fixdt(1,16,0), or a custom <data type expression>.

Block Characteristics

Data Types	double | fixed pointa | single
Multidimensional Signals	yes
Variable-Size Signals	yes
a Signed only.

More About

Input-to-Output Dimensions

The OSTBC combiner supports time and spatial domains for OSTBC transmission and an optional dimension over which the combining calculation is independent. This illustration indicates the supported input dimensions and resulting output dimensions.

This table shows the supported input and output dimensions, which depend upon the values of F and M.

Values of F and M	Rx Input	cEst Input	Output
F = 1 and M = 1	Column vector	2-D	Column vector
F = 1 and M > 1	2-D	3-D	Column vector
F > 1 and M = 1	2-D	3-D	2-D
F > 1 and M > 1	3-D	4-D	2-D

• R — Symbol rate of the code, as specified by the Rate parameter.

  • For N = 2, R must be 1.

  • For N = 3 or 4, R can be 3/4 or 1/2.

• N — Number of transmit antennas must be 2, 3, or 4, and is specified by the Number of transmit antennas parameter.

• M — Number of receive antennas must be an integer in the range [1,8], and is specified by the Number of receive antennas parameter.

• T/R — Input symbol sequence length for the time domain. The time domain length T/R must be a multiple of the number of symbols in each codeword matrix.

  • For N = 2 or R = 1/2, T/R must be a multiple of 2.

  • For R = 3/4, T/R must be a multiple of 3.

• T — Symbol sequence length in time domain for the output signal.

  • For N = 2, T is a multiple of 2.

  • For N = 3 or 4, T is a multiple of 4.

• F — Additional dimension; typically the frequency domain. The combining calculation is independent of this dimension. F can be any positive integer.

Fixed-Point Signals

To highlight the data types used for fixed-point signals, use this equation for $${\widehat{s}}_1$$ for Alamouti code with one receive antenna:

$${\widehat{s}}_1=\frac{h_{1,1,}^{*}{r}_{1,1}+h_{2,1,}r{}_{2,1}^{*}}{{}^{{\Vert H\Vert }^2}}=\frac{h_{1,1,}^{*}{r}_{1,1}+h_{2,1,}r{}_{2,1}^{*}}{{}^{h_{1,1}{h}_{1,1,}^{*}+h_{2,1,}{h}_{2,1}^{*}}}$$

In this equation, the data types for the Product output and Accumulator parameters correspond to the product and summation in the numerator. Similarly, the types for the Energy product output and Energy accumulator parameters correspond to the product and summation in the denominator.

Signal Flow Diagram for s₁ Combining Calculation of Alamouti Code with One Receive Antenna

This equation shows the data types that the OSTBC combiner uses for fixed-point signals in the Alamouti code when the number of receive antennas, M, is greater than one.$${\widehat{s}}_1=\frac{h_{1,1,}^{*}{r}_{1,1}+h_{2,1,}r{}_{2,1}^{*}+h_{1,2}^{*}{r}_{1,2}+h_{2,2}r{}_{2,2}^{*}+\mathrm{...}+h_{1,M,}^{*}{r}_{1,M}+h_{2,M}r{}_{2,M}^{*}}{h_{1,1}{h}_{1,1}^{*}+h_{2,1}{h}_{2,1}^{*}+h_{1,2}{h}_{1,2}^{*}+h_{2,2}{h}_{2,2}^{*}+\mathrm{...}+h_{1,M}{h}_{1,M}^{*}+h_{2,M,}{h}_{2,M}^{*}}$$

Signal Flow Diagram for Complex Multiply of a + ib and c + id

For binary point scaling, you cannot specify WL_p and FL_p. Instead, the block determines these values implicitly from WL_a and FL_a.

The internal rule for the Product output and Energy product output parameters are:

• When you select Inherit via internal rule, the internal rule determines WL_p and FL_p. Therefore, WL_a = WL_p + 1 and FL_a = FL_p

• For Binary point scaling, you specify WL_a and FL_a. Therefore, WL_p = WL_a – 1 and FL_a = FL_p.

For information on how the internal rule applies to the Accumulator and Energy Accumulator parameters, see Inherit via Internal Rule.

Algorithms

OSTBC Combining Algorithm

The OSTBC combiner algorithm implements the five different OSTBC combining computation matrices shown in this table. The number of transmit antennas and the symbol rate determine the codeword matrix that the algorithm uses to combine the received signal.

Number of Transmit Antennas	Rate	Computational Algorithm per Codeword Block Length
2	1	$$\left(\begin{array}{c}{\widehat{s}}_1\\ {\widehat{s}}_2\end{array}\right)=\frac{1}{{}^{{\Vert H\Vert }^2}}{\displaystyle \sum _{j=1}^M\left(\begin{array}{c}{h}_{1,j}^{*}r{}_{1,j}+h_2{,}_{j}r{}_{2,j}^{*}\\ h_{2,}^{*}{}_{j}r{}_{1,j}-h_1{,}_{j}r{}_{2,j}^{*}\end{array}\right)}$$
3	1/2	$$\left(\begin{array}{c}{\widehat{s}}_1\\ {\widehat{s}}_2\end{array}\right)=\frac{1}{{}^{{\Vert H\Vert }^2}}{\displaystyle \sum _{j=1}^M\left(\begin{array}{c}{h}_{1,j}^{*}r{}_{1,j}+h_{2,j}r{}_{2,j}^{*}+h_{3,}^{*}{}_{j}r{}_{3,j}\\ h_{2,}^{*}{}_{j}r{}_{1,j}-h_{1,j}r{}_{2,j}^{*}-h_{3,j}r{}_{4,j}^{*}\end{array}\right)}$$
3	3/4	$$\left(\begin{array}{c}{\widehat{s}}_1\\ \begin{array}{l}{\widehat{s}}_2\\ {\widehat{s}}_3\end{array}\end{array}\right)=\frac{1}{{}^{{\Vert H\Vert }^2}}{\displaystyle \sum _{j=1}^M\left(\begin{array}{c}{h}_{1,j}^{*}r{}_{1,j}+h_{2,j}r{}_{2,j}^{*}-h_{3,j}r{}_{3,j}^{*}\\ h_{2,}^{*}{}_{j}r{}_{1,j}-h_{1,j}r{}_{2,j}^{*}-h_{3,j}r{}_{4,j}^{*}\\ h_{3,j}^{*}r{}_{1,j}+h_{1,j}r{}_{3,j}^{*}+h_{2,j}r{}_{4,j}^{*}\end{array}\right)}$$
4	1/2	$$\left(\begin{array}{c}{\widehat{s}}_1\\ {\widehat{s}}_2\end{array}\right)=\frac{1}{{}^{{\Vert H\Vert }^2}}{\displaystyle \sum _{j=1}^M\left(\begin{array}{c}{h}_{1,j}^{*}r{}_{1,j}+h_{2,j}r{}_{2,j}^{*}+h_{3,j}^{*}{}_{3,j}r{}_{3,j}+h_{4,j}r{}_{4,j}^{*}\\ h_{2,}^{*}{}_{j}r{}_{1,j}-h_{1,j}r{}_{2,j}^{*}+h_{4,j}^{*}r{}_{3,j}-h_{3,j}r{}_{4,j}^{*}\end{array}\right)}$$
4	3/4	$$\left(\begin{array}{c}{\widehat{s}}_1\\ \begin{array}{l}{\widehat{s}}_2\\ {\widehat{s}}_3\end{array}\end{array}\right)=\frac{1}{{}^{{\Vert H\Vert }^2}}{\displaystyle \sum _{j=1}^M\left(\begin{array}{c}{h}_{1,j}^{*}r{}_{1,j}+h_{2,j}r{}_{2,j}^{*}-h_{3,j}r{}_{3,j}^{*}-h_4^{*}{}_{,j}r{}_{4,j}\\ h_{2,}^{*}{}_{j}r{}_{1j}-h_{1,j}r{}_{2,j}^{*}+h_4^{*}{}_{,j}r{}_{3,j}-h_{3,j}r{}_{4,j}^{*}\\ h_{3,}^{*}{}_{j}r{}_{1j}+h_{4,j}^{*}{}_{}r{}_{2,j}+h_{1,j}r{}_{3,j}^{*}+h_{2,j}r{}_{4,j}^{*}\end{array}\right)}$$

• $${\widehat{s}}_k$$ represents the estimated kth symbol in the OSTBC codeword matrix.

• h_ij represents the estimate for the channel from the ith transmit antenna and the jth receive antenna.

  • Values for i must be in the range [1,N], where N is the number of transmit antennas.

  • Values for j must be in the range [1,M], where M is the number of receive antennas.

• r_lj represents the lth symbol at the jth receive antenna per codeword block.

  • Values for l must be in the range [1,L], where L is the codeword block length.

• $${\Vert H\Vert }^2$$ represents the summation of channel power per link. Specifically, $${\Vert H\Vert }^2={{\displaystyle \sum _{i=1}^N{\displaystyle \sum _{j=1}^M\Vert h_{ij}\Vert }}}^2.$$

  • Values for l must be in the range [1,L], where L is the codeword block length.

  $${\Vert H\Vert }^2$$ represents the summation of channel power per link. Specifically, $${\Vert H\Vert }^2={{\displaystyle \sum _{i=1}^N{\displaystyle \sum _{j=1}^M\Vert h_{ij}\Vert }}}^2.$$

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2009a